APPROXIMATION APPROACH IN CERTAIN PROBLEMS OF THE THEORY OF DIRICLET SERIES WITH MULTIPLICATIVE COEFFICIENTS
https://doi.org/10.22405/2226-8383-2016-17-4-124-131
Abstract
In this paper we consider a class of Dirichlet series with multiplicative coefficients which define functions holomorphic in the right half of the complex plane, and for which there are sequences of Dirichlet polynomials that converge uniformly to these functions in any rectangle within the critical strip. We call such polynomials approximating Dirichlet polynomials. We study the properties of the approximating polynomials, in particular, for those Dirichlet series, whose coefficients are determined by nonprincipal generalized characters, i.e. finite-valued numerical characters which do not vanish on almost all prime numbers and whose summatory function is bounded. These developments are interesting in connection with the problem of the analytical continuation of such Dirichlet series to the entire complex plane, which in turn is tied with the solution of a well-known Chudakov hypothesis about every generalized character being a Dirichlet character.
About the Authors
V. N. Kuznetsov
Saratov State University
Russian Federation
Russian Federation
Dr. of techical science, Professor, Head of Department of Computer Algebra and Number Theory
O. A. Matveeva
Saratov State University
Russian Federation
Russian Federation
Ph.d. in Physical Mathematical Sciences, assistant at Department of Computer Algebra and Number Theory
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Review
For citations:
Kuznetsov V.N., Matveeva O.A. APPROXIMATION APPROACH IN CERTAIN PROBLEMS OF THE THEORY OF DIRICLET SERIES WITH MULTIPLICATIVE COEFFICIENTS. Chebyshevskii Sbornik. 2016;17(4):124-131. (In Russ.) https://doi.org/10.22405/2226-8383-2016-17-4-124-131
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